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Saturday, June 23, 2018

Siobhan Roberts, Canadian author and science journalist on books about the brilliant 18th-century mathematician Leonhard Euler.

Photo: Peter and Maria Hoey

A few years ago, a mathematician and a
neuroscientist led a study investigating “the experience of mathematical
beauty and its neural correlates.” The methodology rolled 14
mathematicians into a functional magnetic resonance imaging machine and
asked them to view and rate a collection of 60 mathematical formulas
that they had previously assessed as beautiful, neutral or ugly.
(Detractors of this sort of study call it “neurotrash,” but no matter.)
While viewing the more aesthetically pleasing specimens, the
mathematicians’ fMRI results showed activity in the “emotional brain,”
specifically field A1 of the medial orbito-frontal cortex—the same area
stimulated by moral, musical and visual beauty. Sometimes the
mathematicians exited the machine weeping.

The equation that consistently rated the most beautiful was a
famously compact specimen devised in the 18th century by the Swiss
mathematician
Leonhard Euler
: e iπ + 1 = 0.Euler’s equation
links—via three basic arithmetic operations, each deployed only
once—five fundamental mathematical constants: 0, 1, i (the square root of -1, aka the “unit imaginary number”), π and e
(“Euler’s number”—2.71828 . . . —which is linked to exponential
growth). It is sometimes called Euler’s identity, or Euler’s formula,
but by whatever name it is currently having something of a moment.

Two new books pull apart the equation—deconstructing it technically and historically—and celebrate its niftiness: “A Most Elegant Equation” (Basic, 221 pages, $27) by
David Stipp
and “Euler’s Pioneering Equation” (Oxford, 162 pages, $19.95)
by
Robin Wilson.
Mr. Stipp’s roving account is propelled by his folksy sense of
humor, and, as the author himself admits at one point, by “giddy
metaphorical overreach.” Mr. Wilson’s account is more no-nonsense,
proceeds on a shorter mathematical tether and has a quieter epigrammatic
levity.

Both books, by way of introduction, mention the neuroscience study,
and both lean on the Stanford mathematician
Keith Devlin
for this pronouncement: “Like a Shakespearean sonnet that
captures the very essence of love, or a painting that brings out the
beauty of the human form that is far more than just skin deep, Euler’s
equation reaches down into the very depths of existence.” Both also
quote the physicist
Richard Feynman,
who at age 14 wrote in a notebook that Euler’s equation was “the
most remarkable formula in math.”

Convinced yet? If you aren’t by
all this anecdotal testimony about the formula’s pure beauty, then
consider its applied incarnations.Read more...

A Most Elegant EquationBertrand Russell wrote that mathematics can exalt "as surely as poetry."
This is especially true of one equation: ei(pi) + 1 = 0, the brainchild
of Leonhard Euler, the Mozart of mathematics.

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Hello, my name is Helge Scherlund and I am the Education Editor and Online Educator of this personal weblog and the founder of eLearning • Computer-Mediated Communication Center.
I have an education in the teaching adults and adult learning from Roskilde University, with Computer-Mediated Communication (CMC) and Human Resource Development (HRD) as specially studied subjects. I am the author of several articles and publications about the use of decision support tools, e-learning and computer-mediated communication. I am a member of The Danish Mathematical Society (DMF), The Danish Society for Theoretical Statistics (DSTS) and an individual member of the European Mathematical Society (EMS). Note: Comments published here are purely my own and do not reflect those of my current or future employers or other organizations.